In a medium bowl combine the apples, with the brown and white sugar. Add flour and cinnamon and continue mixing until they are well coated. Using the 'Miracle Pie Crust' recipe on this page, roll out two even pie crusts. Put one crust in the bottom of a 9-inch pie pan and add the apple mixture made above. Dot the apple mixture with small dabs of butter. Top with another pie crust and cut slits. Beat one egg and brush the entire pie crust with egg for browning. Preheat oven to 350 degrees and bake for 50 minutes.